Average Error: 39.7 → 0.1
Time: 12.5s
Precision: 64
Internal Precision: 1344
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{e^{x} + 1}\]

Error

Bits error versus x

Derivation

  1. Initial program 39.7

    \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]

  2. Applied simplify0.1

    \[\leadsto \color{blue}{\sqrt{e^{x} + 1}}\]

Runtime

Time bar (total: 12.5s)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))